Soil Mechanics

Philosophy of Soil Mechanics

Posted in Critical State Soil Mechanics, On Paradigm Shifts, Scholasticism by Paul Joseph on February 23, 2017

There is a branch of philosophy called “philosophy of science.” In case you are bored, you should try a course in it–it is well worth it. I recap below, key understandings from philosophy of science, specifi­cally targeting them to soil mechanics in general and critical state soil mechanics (CSSM) in particular. If you can’t take a college course in the philosophy of science, I strongly recommend this audio course–it is very good! I was lucky enough to be able to borrow it from my local library. It isn’t easy I have to say–I had to listen to it three times be­fore I felt I understood its key points.

FALSIFIABLE: The first question to ask when presented with a the­ory is this: does it have a falsifiable hypothesis. If it does, then the concept or theory is scientific. In the 1950’s the world famous phi­losopher of science Karl Popper defined a scientific theory to be a theory founded on a falsifiable hypothesis, a definition which since then has been taken for granted.

IF a theory does not have a falsifiable hypothesis, then like it or not, the theory is not scientific. A theory without a hypothesis is like a fortress without a well; a theory without a falsifiable hypothesis is a fortress whose well will soon run dry. Remarkably, even today, more than half a century later, most academics in soil mechanics seem unaware of the implications of this statement, and one finds expensive books written on theories that cannot be falsified,such as this one!

Andrew Schofield and I have been in communication for the last decade and I have learned much from him as a result. I first met him in the Summer of 1986 at the Cambridge Centrifuge Laboratory, and hold him in high esteem. I read his 2005 book (Schofield, 2005) and strongly recommend that everyone read it. You can read my review of this book, including my detailed critique of CSSM here. Recently (2013), after some discussion between us, Andrew Schofield wrote me that the falsifiable hypothesis for elasto-plastic soil mechanics is that soils can be modeled as metals (molten). If so, then this hypothesis has indeed been falsified–it can be readily shown NOT to match commonly available empirical data on ordinary soils.

The basis of this hypothesis is the Drucker-Prager criterion first proposed in 1952 by the two mathematicians Daniel C. Drucker and William Prager in a short eight page note in a journal of mathematics (see Drucker and Prager, 1952). This failure criterion was for materials idealized as having no structure. In their note Drucker and Prager also showed how to use their theory to calculate the critical height of a vertical cut in clay, using plane and log spiral failure surfaces. Roscoe, Schofield, and Wroth in the soil mechanics department of Cambridge University enthusiastically embraced Drucker and Prager’s approach.

This ability to readily falsify the hypothesis that soils can be mod­eled as materials with no structure and implicitly constituted of iso­tropic point particles was identified as soon as the theory was first adapted for soils in the 50’s and 60’s. Alan Bishop of Imperial Col­lege used to routinely demonstrate that CSSM and elasto-plasticity theory did not stand up when applied to real soils (Niechcial, 2002). The reason for this (as you will see below) is because Drucker and Prager criterion as applied to soils are at root, scholastic–not taking into account the fundamental, empirical fact that soils are particulate materials (not point particles) with particles that have explicitly aniso­tropic properties (not isotropic). Drucker and Prager’s (and An­drew Schofield’s) premise that soils can be modeled as metals (molten) with implicit isotropic point particles is not found true, ex­cept as a very crude approximation–a scholastic idealization. Sir Alec Skempton, the “founding father” of British soil mechanics, attributed the scholastic nature of CSSM to Roscoe, of whom he said: “… he did little field work and was, I believe, never involved in a practical engi­neering job.” (Niechcial, 2002).

Most papers on CSSM models follow along in this scholastic ap­proach–when they prove their model, use a “simple clay,” i.e., a pure CH material. They run a few tests on normally consolidated samples or samples at a low OCR to get a simple stress-strain curve with no strain-softening. The sample chosen is usually an “insensitive” clay, i.e., a clay that exhibits no stress-strain softening. This simple stress-strain curve is then shown to be matched by the model.

But falsifiable does not mean seeking “confirmation.” I can run a thousand tests that create simple stress-strain curves with little to no strain-softening, and show that my model matches the empirical evi­dence (the test data). However this is not an attempt at falsification–rather it is the opposite–an attempt at confirmation.

Scientific theories are not tested this way–rather, falsification means to try every which way to break the model and to see where it fails. A true attempt at falsifying the theory would be to model realis­tic stress-strain curves that show strain-softening, to match the accom­panying pore-pressure (or void-ratio) changes. The test would be on a soil with a wide range of grain sizes–not an insensitive clay that is al­most guaranteed to generate a simple stress-strain curve.

Attempts have been made using CSSM based elasto-plastic soil models to match complex stress-strain curves from real soils (those with a mixture of grain sizes) and the results have been abysmal–a complete failure to match strain-softening curves beyond peak strength. So yes, CSSM theory has indeed been falsified, other than for the simplest stress-strain curves from soils (CH and also, CL soils) that do indeed resemble soft metals.

Further, most CSSM models violate the laws of thermodynamics (a big no-no in and of itself). Later on, you in this chapter you will read about hyperplasticity–a theory that does not violate these laws. However, hyperplasticity is based on a non-falsifiable ­hypothesis–the Ziegler Orthogonality Condition.

We know that a theory that is either falsified or which is not falsi­fiable is not a scientific theory. A theory that is not scientific, but which is presented as if it is, meets the standard definition of a pseu­doscience (see Hansson, 1996). Metals based theories of plasticity as applied to soils being either already falsified, or based on non-­falsifiable theory, but yet which are taught as if they are scientific, count as pseudoscience. More on this later in this chapter.

SIMPLE: A second test to apply when comparing two theories is Oc­cam’s razor – which theory is simpler while yet explaining all the facts? By any measure, DSSM is very simple – in fact one mathemati­cian I presented it to called it … yes you got it…”very simple.” It needs simple hypotheses (Poisson process, simple friction, dynamical sys­tem) based on transparent underlying physical phenomenon and one equation to directly formulate the numerical model. Truly, as New­ton said some five hundred years ago, Nature is simple, and always consonant to itself.

Note: It is very important to note that this simplicity results primarily be­cause we do not consider inertial effects of individual particles, i.e., effects of the mass of individual particles as they collide against each other during defor­mation. This is simply because strain-rates in traditional soil mechanics prob­lems are small enough to where we can ignore these effects. Once you consider grain inertial effects, the complexity goes up by an order of magnitude at least. In 1997 as part of my “wild hunt” for evidence that I was dealing with a dy­namical system, I came across a paper in the journal Nature that modeled particles in a fluidized bed furnace, an environment where the velocities are very high and the particulate densities very low, so that the particles are sus­pended in gas or fluid and where consequently, inertial effects play a role along with temperature and aerodynamic effects. The paper described the resultant chaotic dynamics that occur. The mathematics was extremely complicated, but yet the paper gave me a huge sense of relief–I knew now for sure, that at least at very high velocities and very low densities, chaotic behavior existed in particulates and that there were other fields that considered this as nothing new. I no longer have that Nature paper, but you can find similar papers quite easily on the internet–see for example this one.

PARSIMONIOUS: Good theories are also parsimonious theories–they should require a minimum of words and equations to explain them. The DSSM model is based on a hypothesis that is six words long (a Poisson process drives soil behavior), is expressed by one set of equations that explains all the known behaviors of soil including the log-linear consolidation curve. This contrasts with CSSM that needs upwards of 50 equations and many strange, artificial properties, and which takes the log-linear consolidation curve, a fundamental and basic relationship in soil mechanics, to be a given.

EXPLAIN: A third test of a theory is its explanatory power. We saw that DSSM theory explains things previously mysterious – for exam­ple why in one-dimensional consolidation, void ratio must vary lin­early with the log of the effective vertical stress or why  should be approximately constant for a wide range of soils. I am not aware that CSSM has explained anything per se. CSSM is at best, only a de­scriptive theory – for ­example, it simply takes the linear relationship between void-ratio and the log of the effective vertical stress as a given.

PREDICT: A fourth test to apply to a theory is how many new and surprising things does it predict? As we saw Chapter 4 of the DSSM book pre­dicts on the basis of entropic principles what the distributions of in­terparticle contact areas should look like at the initial condition and at the steady-state. I am not aware that CSSM makes any predictions, novel or otherwise. In fact, soil mechanics, being dominated to date by CSSM, is a stark contrast to subjects like physics.

In physics, theories exist that are powerful enough to make pre­dictions with. Hence in physics, theory based predictions usually lead experimental verification. Recall the recent discovery of the Higgs Boson–a multi-billion dollar search that was driven by a predic­tion made almost half a century ago based on theory! In stark con­trast, in soil mechanics, the reverse is the case. For example prior to the advent of DSSM, no theory predicted the experimental findings by Mesri that  is approximately constant or that the EOP curve obtained from static incremental one-dimensional loading is unique. Till the advent of DSSM, there was no theory to explain Mesri’s ex­perimental obervations even ex post facto. DSSM shows why these two relationships must hold (see Chapter 7 of the DSSM book) .

MATCH: A fifth (and essential) test is to see how well does the model that derives from the theory fit the actual data. Recall from Chapter 1 of the book  that our motto is: test predictions with experiments! Remember ­Richard Feynman and his eloquent statement: “You may have the most beautiful and elegant theory in the world, but if the model that re­sults from it does not fit the data–then your theory is simply wrong!” Of course, CSSM is notorious for the tremendously poor fits it provides to stress-strain and void-ratio strain curves with strain-softening. CSSM seems to fall into a limbo of being neither right or wrong. It brings to mind the story told of another Nobel Prize winning physicist, Wolfgang Pauli, who when presented by his friend with a theory remarked: “Das ist nicht nur nicht richtig, es ist nicht einmal falsch!” (“This isn’t right. This isn’t even wrong!”).

Any mismatch should not be excused away. Recall from Chapter 3 of the book that the DSSM parameters were obtained from sets of stress-strain curves that went far past failure including those points measured long after failure planes had developed in the sample. Re­call also that the fits were very good for the entire curve, right to the end, well past the point when failure planes developed. Recall also that what this means is that the DSSM equations are tracking condi­tions on the dominant failure plane, past failure, past the develop­ment of failure planes, and is able to do it very well (witness the high chi values). This contrasts with CSSM that is quite unable to track conditions once failure planes develop. In fact, the development of failure planes is given as the chief reason (excuse) why CSSM based models are unable to track conditions post failure.

Imre Lakatos, a noted philosopher of science coined the term “degenerate research program” for theories where excuses are used to justify an inability of theory to match empirical data. Lakatos was commenting in general about scientific programs and probably did not even know that a field like soil mechanics existed, which makes his comments all the more powerful. DSSM needs no excuses as it is able to track conditions post failure plane development. CSSM on the other hand qualifies as a “degenerate theory” given its need for excuses about its inability to match the empirical evidence (test data).

TRANSPARENT (PORTABLE): Good theories have a transparent physical basis–for example, when using DSSM, the underlying physi­cal phenomenon (Poisson process, simple friction, dynamical system) are clear, always present, and easy to understand. The more basic the underlying phenomena that drive the model, the more “portable” the model is–by this I mean, the easier it is to explain the model to someone in a different field, but who is aware of the fundamental physical principles that the model rests on–in this case, basic friction, Poisson processes, and dynamical systems theory. For example, I was able to explain the DSSM model quite comprehensively to an Electri­cal engineer, in less than an hour!

This contrasts with CSSM where one requires a lot of arcane spe­cialized knowledge and background to figure out what is going on in the first place. The CSSM models are complex and not portable–in the midst of all the equations, one loses sight of the physical basis of many of the idealizations that CSSM makes. And if one works on something else for say a year and then returns to it, it is hard to figure out once again some of the arcane CSSM models with their relatively arbitrary assumptions, and naive and questionable idealizations.

One example of such naive and questionable idealizations is a key assumption made by many CSSM models, namely that pure hydro­static stress results in no shear strains. This is absurdly wrong – a soil structure can be analogized (thought of) as a “house of cards” much like what we used to build when we were little children. Applying pure hydrostatic stress to a house of cards will cause shear deforma­tion, and the structure to collapse. Even small children know this intuitively.

Truly, any version of CSSM that assumes pure hydrostatic stress causes no shear strains is indeed a house of cards, fundamentally flawed from the very get-go! Such models indicate their authors do not have a physical feel for the nature of soil and soil structure. Andrew Schofield has told me many times that try hard though he did, he was never able to put soils into pure hydrostatic compression. You can read about it in Schofield (2005) also.

The reason such a flawed, artificial assumption is made is that numerical instabilities occur in elasto-plastic finite element models if it is assumed that pure hydrostatic forces also cause shear strains. It seems to me this assumption of zero shear strain under pure hydro­static compression is an example of the dangerous idealizations that I mentioned earlier. If you do a FEM analysis, please do confirm that your model does not make this assumption. If you find it does, dump the model ASAP!1 In a court case it is easy for a lawyer to convey to a jury made up of non-technical people, the error in assuming zero shear strains under pure hydrostatic stress, using the “house of cards” analogy above. This can work to your advantage/disadvantage de­pending on which side of the case you are on.

Models that make artificial assumptions which do not match un­derlying physical phenomena often can be traced to academics who have not physically interacted soils since they left graduate school, and who consequently lack a physical feel for soils. As I wrote in a footnote in Chapter 2, I believe that one obtains this “physical feel” in a quite literal sense only after one has extensively interacted physi­cally with the object of ones ­introspection, using one’s hands and not by merely doing “analysis” or “design.” One cannot expect elasto-plas­tic theories derived originally for metals that implicitly assume the material being modeled to be made of isotropic point particles, to provide good results when applied to materials composed of irregular, finite-sized particles, with inherent anisotropic properties.

Note: In 1980, one of the first questions I asked my soil mechanics professor S. V. Ramaswamy was why soils were being treated as metals. I had just turned 20, and by this time, my brother and I had been tuning two-stroke motorcycles for racing, for several years. At that time in India, motorized metal grinders were not cheap and so we had to use ordinary metal hand files to raise or lower the two-stroke intake, transfer and exhaust ports. The experi­ence of grinding cast iron manually was for me, simply put, a huge shock. Only when I took 8 hours to lower the exhaust port by a mere 3 mm did I realize how hard a metal (then too a relatively soft metal like cast iron) really was. Only when I saw the fine iron powder, in which it was impossible to discern any different shapes of the iron powder particles without a microscope, did I realize what an atom must be. Hence when in undergraduate class, I was told soils were modeled at metals, I was instinctively and immediately taken aback–the idea struck me as simply absurd–hence my question. It was Professor Ramaswamy who told me that it was possibly because of his train­ing as a mechanical engineer, as well as the lack of any alternate theory, that made Roscoe amenable to suggestions of modeling soils as metals. Today, al­most thirty-five years later, I realize the importance of my experience filing metal with a hand file for eight hours. This is exactly why I admire Nietzche’s saying: The doer alone learnth. As with metals, so also with soils! Hands on contact is essential to obtain a physical feel for the object of study and to truly understand! Today, sadly, most academics lack this “physical,” hands on training, and hence are too quick to accept bizarre statements like: “soils are really metals in disguise.” Should you listen to my interview of Steve Poulos you will see how Cassagrande handled this issue. And as it hap­pened with Steve, so also it happened with me. A relatively recent New York Times non-fiction best-seller that captures this viewpoint is: Shopcraft as Soul­craft: An Inquiry into the Value of Work. I think this book is essential read­ing if you want to become really good in soil mechanics! Ramaswamy helped me understand what Roscoe and the “metal” people knew but which I didn’t then–that at very high stresses, metals indeed behave like “modeling clay.” But what I intuitively realized then and which Roscoe and his “metal” people did not seem to (or at least, to this date are not able to realize in their model) is that while metals are made up of isotropic chemical molecules, i.e., isotropic point particles, real soils are not so–they are not point particles and have very anisotropic shapes. This seemingly trivial difference is the heart of the matter, the very core of it. Models that do not account for this core property of soil grains are bound to fail, just as current “metal” models of soils have failed. This is because anisotropic grains created structure that resembles a “house of cards.” And it is this structure that controls behavior. Metal based theories of soil do not capture the behavior of card like structure resulting from this core property of grains–that they are anisotropic at the particle level. Conse­quently, such metal plasticity based models are fundamentally broken at their very center. Attempts to directly model such card like structure will result in extremely complicated mathematics. DSSM on the other hand doesn’t need to model this structure directly because the net effect of this structure is a friction based Poisson process. This, DSSM models directly.

There is a long tradition in the general sciences (other than soil mechanics) of theories that come and do a poor job of things. As I noted before, a famous philosopher of science, Imre Lakatos, coined the phrase “degenerate research program” to describe such theories. According to Lakatos, a degenerating research program is a scientific enterprise that started out with great promise, showing impressive results in a limited domain. Researchers then apply the program more generally. At this point, if they succeed, the program gains more followers and expands and is not degenerate. However, on the other hand, if researchers encounter important anomalies that consistently resist explanation with the new concepts, then the program will stag­nate. It will be characterized by a lack of growth, or growth of a pro­tective belt of auxiliary hypotheses.

Lakatos was almost certainly completely unaware of the existence of a subject called soil mechanics. Nonetheless, it seems to me that CSSM, with its protective belt of auxiliary hypotheses (excuses) such as failure planes or non-uniform particles or anisotropy or lack of shear under pure hydrostatic stress, or local non-linearity of very early stress-strain behavior, etc., etc. to explain away poor fits to real data, qualifies itself as one of ­Lakatos’s degenerate research programs. Worse, his comments on pseudoscience seem also ­applicable to CSSM.

You have reached the end of the course. One last assignment though! … stop for a minute … visualize the Poisson process of soil deformation … then from understanding (and not because you sim­ply memorized it), write out the single set of three equations that di­rectly describe how the deformation occurs. Well done! You have fully, and comprehensively described the fundamental mechanism of soil deformation.

Now step back in your mind and compare what you just did to the over 50 equations that it takes to define CSSM. Recall too that the CSSM model provides very poor fits to the test data, and that we really have no physical understanding of what the central, falsifiable hypothesis of CSSM is. Recall also, that CSSM is not able to derive that most fundamental relationship in soil-mechnics–the linear rela­tionship between void-ratio and vertical stress in one-dimensional consolidation. Nor can it explain why  is approximately con­stant nor why the EOP curve obtained from static incremental one-dimensional loading is unique.but simply takes these as given. Recall that CSSM makes no new, novel predictions. Which model do you now believe? I personally believe that CSSM is a failed and broken theory–a dead end, a red-herring in the history of soil mechanics.

The question then arises–why has the soils community stuck with CSSM for so long? The reasons are two. First, till now, there has been no alternate theory. This reminds me of the well known story where a policeman saw a man searching for something under a lamppost. “What have you lost?” the policeman asked. ” My keys,” said the man. The policeman then helped the man look. After searching for a while he asked the man: “Where exactly did you drop them?” “Over there,” responded the man, pointing towards a dark street a good distance away. The policeman asked exasperatedly “Why are you looking here if you lost your keys over there?” The man replied “Because the light is so much brighter here.”

So too with CSSM; absent any alternative, the soils community had no choice. Hopefully, the advent of DSSM provides an alterna­tive, and now the search can proceed where the keys really are!

The second reason for CSSM is that, yes, crudely, very very crudely, a fine grained, homogenous material, lacking in structure, somewhat does resemble a soft metal. As I mentioned above, I first heard this in the Spring of 1980 from my undergraduate soil mechan­ics teacher–Prof. S. V. Ramaswamy. He was the first to suggest to me that perhaps Roscoe naturally analogized soils with metals because he was a Mechanical engineer by training. In the 1950’s, when CSSM was birthed, most triaxial tests were on fine grained clays, remoulded and reconsolidated isotropically. Such tests generate simple stress-strain-volume curves and scarcely exhibited strain-softening; indeed their behavior can be crudely approximated by a metals theory of plasticity.

DruckerPragervon Mises were all applied mathematicians who worked on modeling solid materials, particularly metals in plastic yielding (analogous in their plastic state to a molten metal). In the late 50’s, the Cold War was being waged in earnest and metals based elasto-plastic models were applied initially to problems in the aero­space industry and later to problems relating to underground nu­clear shelters. Aeronautical engineers were using finite-element analyses on air-frames and there was much talk in engineering circles of this (then) new technique–use of FEM methods and elasto-plastic models to analyze a multitude of engineering problems. For a history of the development of Finite Elements, see Clough and Wilson (1999).

In my opinion, it is no coincidence that Kenneth Roscoe (1914–1970) who trained as a Mechanical engineer, was the first to approxi­mate soil plasticity as metal plasticity. It would have been natural and instinctive for him to be receptive to the idea of soil plasticity as anal­ogous to metal plasticity–an approximation that today, on detailed examination and application, we find holds up only very crudely. Note: this analogy with metals probably holds up best for soils that are pure “fatty” clays (CH). The reason I use the word “pure” is that once you exceed 5% particles larger than clay-size, then it is these larger particles that control behavior. In short, as the percentage of soil greater than clay-size increases, behavior becomes more complex–this is why CSSM models do a very poor job of predicting behavior as the sand content goes up.

As the years went by, soil-fabric level structural effects came into play, either through soils with non-symmetric grain-shapes or larger sized particles, or as a result of an anisotropic fabric obtained through Ko consolidation. Samples began to exhibit strain-softening and very quickly it was realized that CSSM as it was then, provided very poor fits. The band-aid was to add another two dozen or so equations to attempt to address these issues, resulting in some of the murkiest and ugliest mathematics that it has been my karmic misfortune to have had to read. Mathematics like this impresses only “newbies”2 or non-mathematicians! To the formally trained mathematician on the contrary, mathematics of this ugliness has always been a fairly reliable indicator of something being fundamentally broken in the basic approach!

Almost all elasto-plastic models including the various flavors of CAM clay violate basic thermodynamic principles. To correct this a recent (largely since 2000) development in geomechanics has been “hyper-plasticity” with models that satisfy the First and Second Laws of thermodynamics. Hyper-plasticity though is flawed by a fundamen­tal assumption–Ziegler’s Orthogonality Condition (ZOC). ZOC as­sumes a very strong and restrictive version of the Second Law of Thermodynamics–one that is rejected by many as overly restrictive, and if applying at all, then applying only to a narrow subset of materi­als. Further, ZOC remains unproven and it is highly unlikely that anisotropic particles would meet the conditions required of ZOC. Worse, it is a principle which is not testable simply because to date, no one has been able to conceive of an experiment with which to test it.

A recent book (Dawid, R., 2013) discusses string theory in the context of falsifiablity. To date, string theory has not been empiri­cally confirmed, raising the question–is it really science? The world of physics is split into two camps. Thus one camp holds that string theory is to be understood to be a candidate for a final theory, a theory that at a fundamental level accounts for all observable phys­ical phenomena. However most scientific observers fall into the second camp–one that denies any claims of string theory being a final theory, a claim they feel is an indication of the over-optimistic mindset prevalent among string physicists. It remains a philosophi­cal question if a final theory claim makes epistemological sense and if so, whether this spills over to non-final theories such as the ZOC.

In short the fundamental principle on which hyper-plasticicty rests on today cannot be falsified, and as best we know from Karl Pop­per’s work in the 1950’s, a theory that cannot be falsified does not count as scientific. Nonetheless, in (expensive) text books, ­hyper-plasticity is presented as if it is scientific. Many researchers in the general sciences accept Hansson’s (1996) definition for what counts as pseudoscience: “An activity or a teaching has to satisfy the following two criteria: (1) it is not scientific, and (2) its major propo­nents try to create the impression that it is scientific. ” By this stan­dard, it seems to me that hyper-plasticity counts fully as a pseudo-science3.

However, regardless of whether or not hyper-plasticity is a pseudo­science or whether or not the laws of thermodynamics can be met or whether or not ZOC can be proven, the fact remains is that we are still dealing with metal plasticity as applied to soils, i.e., the same old metal-plasticity in new thermodynamically viable bottles! Conse­quently, hyper-plasticity continues to have the same fundamental problem of being unable to match soils that are constituted of non-anisotropic particles because like all current elasto-plstic theories it implicitly assumes that soil particles are point particles. They are not! Soil particles (for anyone who has actually handled real soils) have mass, anisotropic shapes and other anisotropic particle level proper­ties. In other words, in addition to the soil fabric’s “bedding plane anisotropy”, there is the question of particle level anisotropy. Plastic­ity theories with their inbuilt, implicit assumption of point particles (isotropic), are fatally flawed at their very core, regardless of whether or not they meet the laws of thermodynamics.

This can be seen by studying almost any book or paper on elasto-plastic soil models–the scope of the proof is meagre–the attempts are not at falsification using “complex” stress-strain curves that exhibit strain-softening, but rather, are mere demonstrations of confirma­tion using simple stress-strain curves from insensitive soils, typically pure CH or CL-CH soils. As we saw earlier, this is most certainly not the way that theories are validated!

DSSM does not need to make any of the numerous assumptions made by CSSM and elasto-plasticity. In fact, DSSM stands in strong contrast with pseudoscientific soils plasticity theories, as it is falsifi­able at many levels as described in the main body of this course. Hence, DSSM could have been falsified at any of the following points listed ­below–the fact that it wasn’t means that as of now, like any valid scientific theory, it remains to be falsified. Note: any current scientific theory is not true in an absolute sense. All a scientific the­ory says is effectively…” here is our best falsifiable hypothesis that ac­counts for the empirical evidence–so far, no one has been able do disprove it.” This does not mean that at some point in the future some one will not be able to falsify it. When this happens, the theory, like any other scientific theory, has to be either abandoned or modi­fied (while yet retaining falsifiability) to account for the new informa­tion that falsified it originally.

Hence DSSM could have been falsified in the claims made in Chapter 2–that soil shear is a dynamical system, or in Chapter3–that its underlying basis is a Poisson process resting on simple friction or in Chapter 4–that the logarithm of the ratio of peak shear to confining stress varies linearly with the logarithm of OCR and that stress-strain curves normalize or in Chapter 5–that strain-rate effects depend crucially on the dependence on strain-rate of the coefficients of friction at inter-particle contacts, or in Chapter 6–that if DSSM were falsifiable, it would not be able to predict (as it did) the linear relationship in one dimensional consolidation be­tween the void-ratio and the log of the effective vertical stress, or in Chapter 7–that the EOP curve under static loading is unique and that  is indeed approximately constant for a wide range of soils.

The fact that it is falsifiable at these points, but has yet not falsi­fied, indicate that currently, DSSM is a scientific (falsifiable) princi­ple that to date has stood the test of falsifiability. As noted above, this does not mean the theory is complete or even true–no scientific the­ory is really true–all we can say is that to date, it has not been falsi­fied. Also, no scientific theory is complete–one can always drive down to a level where unknowns remain–in our case, the fundamen­tal nature of simple friction remains to be clearly understood even today.

I recently had to review two complex elasto-plastic models, rather well known to those in the field but which I shall not name, one from the US, the other from the UK, and found each to be riven through and through with thumb rules, dangerous idealizations, and un­proven assumptions. Curious about this, I checked out several other models published recently and found that they all had a common feature–the core equations they use for the plastic model, generally some variant of the original Cam clay model with a slight modifica­tion or two. Some appear to have been pulled out of a magician’s hat, coming complete with magical constants, magical starting equations, and magical beliefs.

Thirty years ago in graduate school, I too was very enamored of elasto-plastic models. My views have changed since then as a result of knowledge gained from experience, study, and introspection. To­day I see elasto-plastic soil models as “emperors with no clothes,” just waiting to be challenged in order to be exposed as being nothing but glorified, pseudoscientific thumb-rules or highly theoretic equations that by themselves have not been proven to match the empirical evi­dence, i.e., test data from a wide range of soils. At the heart of each model is a varied combination of approximations, thumb rules, and dangerously idealized assumptions, most, individually unverified over a wide range of soils. If you believe any of these models, do contact me–as they say here in the US to indicate a gullible person: “I’ve got a bridge to sell you.”

Long story short, CSSM is a broken and failed theory, and ac­cording to me, nothing but pseudoscience. If you want me to decon­struct any CSSM model to make this point clear email me using the website for the book information on your model of choice and I shall do so in a post on this site on Deconstructing Elasto-Plastic Soil MEchanics.. I believe the concepts behind these CSSM models are dangerously idealized understandings of soils that originate from academics who have not physically handled for years and with their fingers (I mean this literally), a wide variety of soils and so have never developed a physical feel for soils.

This physical feel can be only developed by years of actually han­dling in ones fingers, a wide variety of soils. Such experience does not come from mere “consulting” or doing “geotechnical design.” Rather it involves physical, intimate, direct, “hands-on” contact with soils, an approach that usually takes at least three to five years of continuous work directly performing field and laboratory tests on soils. Sadly to­day, most academics lack this kind of intense “hands-on” intimate, physical contact with soils, as a result of which some of them create theories that are naive–at best simplistic, at worst, dangerous. Idealizing soil as a metal is one such theory–naive, simplistic, and dangerous!

Note: Should you listen to my interview of Steve Poulos, you will hear that Cassagrande required each of his instructors to ob­tain this hands-on experience by spending at least four years in the Harvard laboratory, running experiments themselves. Little did I know why, but this is the same route that Steve made me follow at GEI–spending about two years in the lab, in addition to the prior three years I had worked in a soils laboratory at a different company!

To repeat, thirty years ago, in my graduate school days, I too strongly believed in CSSM and elasto-plastic soil mechanics. Today however I have come to understand them to be but dead ends. The belief that soils are “really metals” is one that is scholasticism–and to continue to hold it in the face of evidence to the contrary is to be but a scholastic, i.e., someone who adheres to tradition and logic (Aristotelian) and who pays little heed to the (readily avail­able) empirical evidence. I will not be surprised if DSSM replaces CSSM within a generation. As Max Planck famously observed: “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”

Much work remains to be done with DSSM starting with inde­pendent validation of the theory. Additionally, the entire field of soil dynamics remains to be investigated in the light of DSSM. I also be­lieve that concepts from particulate discrete element modelling (see O’Sullivan, 2011 for an overview) complement DSSM and should be leveraged. Hopefully, now that you are have an understanding of DSSM, you will be able to take up this work. Remember this quote, thought to be by Einstein: “If you can’t explain it simply, you don’t understand it well enough.4” So, do not build overly elaborate ­theories–paradoxically, it is far easier to create overly complex theo­ries than simpler theories because usually over complex theories are not fundamental. Consequently, they rarely meet the acid test of a wide range of empirical data. Metals based soil theories are a ­classic example of this.

We started this self-study course with a few words – you will see these again below – but now, hopefully, their meaning is not only clear, but also, self evident!



1. As Soon As Possible

2. American slang for someone who is very new to a field

3. The classic book on pseudoscience is Gardner (1957).

4. Einstein: the life and times (1971) pp. 418 by Ronald W. Clark: Louis de Broglie did attribute a similar statement to Einstein. To de Broglie, Ein­stein revealed an instinctive reason for his inability to accept the purely statistical interpretation of wave mechanics. It was a reason which linked him with the physicist Rutherford, who used to state that “it should be possible to explain the laws of physics to a barmaid.” (note: I have met barmaids (so called) who are geniuses–old Ruthie was prob­ably just another old sexist pig.) Einstein, having a final discussion with de Broglie on the platform of the Gare du Nord in Paris, whence they had traveled from Brussels to attend the Fresnel centenary celebrations, said “that all physical theories, their mathematical expressions apart ought to lend themselves to so simple a description ‘that even a child could understand them.’


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